## Abstract

The image system of singularities of an arbitrary exterior potential field within a triaxial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over the fundamental ellipsoid. The present contribution is a generalization of previous theories on the image system of an exterior potential field within a sphere and spheroid. A proof of T. H. Havelock's spheroid theorem, which apparently is not available in the literature, is also given. The knowledge of the image system is required, for example, when hydrodynamical forces and moments acting on an ellipsoid immersed in a potential flow are computed by the Lagally theorem. The two examples given consider the image system of singularities of an ellipsoid in a uniform translatory motion and in pure rotation. The results are pertinent to ship hydrodynamics.

Original language | English |
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Pages (from-to) | 334-344 |

Number of pages | 11 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - 1974 |